2021 04 21 midterm answers

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Control Systems (Prof. Casella) Midterm Exam – Apr 21st, 2021 ANSWER SHEET Question 1 Consider a standard electrical oven, which has two modes to heat and cook the food. The first mode is by convective heat transfer: electrical heating elements heat up the air in the oven, which in turn heats up the food and the walls of the oven, possibly with the help of a fan. For this heating mode, a thermostat is provided, and the user can set a desired temperature of the air in the oven with a knob. The second mode is by radiative heat transfer: an infrared radiator hanging from the celing of the oven is heated up by the electrical current until it becomes glowing hot, thus heating the food by radiative heat transfer; for this heating mode, the user can set the radiative power with another knob. Classify the control strategy of each of these two modes as either open- or closed-loop, motivating your answer. For each mode, clearly identify the manipulated variable, the disturbance(s) and the controlled variable, and draw a block diagram showing the connections between the plant and the controller. In the case of convective heating, the controlled variable is the oven temperature T, which is measured by a thermometer, the manipulated variable is the electrical power W supplied to the heating elements (or some quantity related to it, e.g. the resistance of the heating elements), the main disturbances are the negative heat inputs Q due to the heat losses to the ambient, the openings of the oven door, and the insertion of cold food in the oven. The control strategy is clearly closed-loop, since the thermostat compares the measured oven air temperature with the value set by the temperature set point knob, and actuates the power accordingly. In the case of radiative heating, the…